Accurate and Approximate Values

If f( θ ) = 10 sin2(0.4 θ– 0.1) show thatand evaluate correct to 3 decimal places.2. Differentiate the following functions:(i)(ii)3. A sound wave is given by the functionWrite down the first four terms of the power series expansions of e–2t and cos 4t.Determine the cubic (up to and including the third power of t) approximation of f(t) and calculate the accurate and approximate values of f(0.02) giving your results correct to 3 decimal places.4. Obtain f ′′(0.3) for each of the following functions:(i)(ii)(iii)Give your answers correct to 4 decimal places.